First go into your Seller Admin > Cart Shipping Settings screen. There, you can enter a Cost for various packaging types. Once you've set up a range of costs, click Next to save changes and proceed to the Shipping Rules screen. If you have anything listed in the Existing Shipping Rules menu, select and delete them, then click Back to Admin.
When you enable Shipping/Buyer's Address in a product's settings, click Next until you reach the Shipping Options screen, where you can specify the packaging type that product ships in and how many units of that product will fit in that type of package (i.e., how many units can be shipped together for the same shipping Cost that you assigned to that package type). Then click Next until you can click Submit to save changes.
There's also another, perhaps easier, way you could go about this, if you simply want to set a flat shipping charge for each unit of each product. Instead of defining Costs for various packaging types, you'd leave all the settings blank or 0.00 on that first Cart Shipping Settings screen, then click Next, and create one Shipping Rule using "Price per unit weight" with a rate of 1.00. Then when you enable Shipping for each product, you'd simply set its Weight to equal the flat-rate that each unit of that product should cost to ship.